MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { eq(X, Y) -> false()
  , eq(n__0(), n__0()) -> true()
  , eq(n__s(X), n__s(Y)) -> eq(activate(X), activate(Y))
  , activate(X) -> X
  , activate(n__0()) -> 0()
  , activate(n__s(X)) -> s(X)
  , activate(n__inf(X)) -> inf(X)
  , activate(n__take(X1, X2)) -> take(X1, X2)
  , activate(n__length(X)) -> length(X)
  , inf(X) -> cons(X, n__inf(s(X)))
  , inf(X) -> n__inf(X)
  , s(X) -> n__s(X)
  , take(X1, X2) -> n__take(X1, X2)
  , take(s(X), cons(Y, L)) ->
    cons(activate(Y), n__take(activate(X), activate(L)))
  , take(0(), X) -> nil()
  , 0() -> n__0()
  , length(X) -> n__length(X)
  , length(cons(X, L)) -> s(n__length(activate(L)))
  , length(nil()) -> 0() }
Obligation:
  runtime complexity
Answer:
  MAYBE

None of the processors succeeded.

Details of failed attempt(s):
-----------------------------
1) 'WithProblem (timeout of 60 seconds)' failed due to the
   following reason:
   
   Computation stopped due to timeout after 60.0 seconds.

2) 'Best' failed due to the following reason:
   
   None of the processors succeeded.
   
   Details of failed attempt(s):
   -----------------------------
   1) 'WithProblem (timeout of 30 seconds) (timeout of 60 seconds)'
      failed due to the following reason:
      
      Computation stopped due to timeout after 30.0 seconds.
   
   2) 'Fastest (timeout of 5 seconds) (timeout of 60 seconds)' failed
      due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'Bounds with minimal-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
      2) 'Bounds with perSymbol-enrichment and initial automaton 'match''
         failed due to the following reason:
         
         match-boundness of the problem could not be verified.
      
   
   3) 'Best' failed due to the following reason:
      
      None of the processors succeeded.
      
      Details of failed attempt(s):
      -----------------------------
      1) 'bsearch-popstar (timeout of 60 seconds)' failed due to the
         following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
      2) 'Polynomial Path Order (PS) (timeout of 60 seconds)' failed due
         to the following reason:
         
         The processor is inapplicable, reason:
           Processor only applicable for innermost runtime complexity analysis
      
   

3) 'Innermost Weak Dependency Pairs (timeout of 60 seconds)' failed
   due to the following reason:
   
   We add the following weak dependency pairs:
   
   Strict DPs:
     { eq^#(X, Y) -> c_1()
     , eq^#(n__0(), n__0()) -> c_2()
     , eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
     , activate^#(X) -> c_4(X)
     , activate^#(n__0()) -> c_5(0^#())
     , activate^#(n__s(X)) -> c_6(s^#(X))
     , activate^#(n__inf(X)) -> c_7(inf^#(X))
     , activate^#(n__take(X1, X2)) -> c_8(take^#(X1, X2))
     , activate^#(n__length(X)) -> c_9(length^#(X))
     , 0^#() -> c_16()
     , s^#(X) -> c_12(X)
     , inf^#(X) -> c_10(X, s^#(X))
     , inf^#(X) -> c_11(X)
     , take^#(X1, X2) -> c_13(X1, X2)
     , take^#(s(X), cons(Y, L)) ->
       c_14(activate^#(Y), activate^#(X), activate^#(L))
     , take^#(0(), X) -> c_15()
     , length^#(X) -> c_17(X)
     , length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L))))
     , length^#(nil()) -> c_19(0^#()) }
   
   and mark the set of starting terms.
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { eq^#(X, Y) -> c_1()
     , eq^#(n__0(), n__0()) -> c_2()
     , eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
     , activate^#(X) -> c_4(X)
     , activate^#(n__0()) -> c_5(0^#())
     , activate^#(n__s(X)) -> c_6(s^#(X))
     , activate^#(n__inf(X)) -> c_7(inf^#(X))
     , activate^#(n__take(X1, X2)) -> c_8(take^#(X1, X2))
     , activate^#(n__length(X)) -> c_9(length^#(X))
     , 0^#() -> c_16()
     , s^#(X) -> c_12(X)
     , inf^#(X) -> c_10(X, s^#(X))
     , inf^#(X) -> c_11(X)
     , take^#(X1, X2) -> c_13(X1, X2)
     , take^#(s(X), cons(Y, L)) ->
       c_14(activate^#(Y), activate^#(X), activate^#(L))
     , take^#(0(), X) -> c_15()
     , length^#(X) -> c_17(X)
     , length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L))))
     , length^#(nil()) -> c_19(0^#()) }
   Strict Trs:
     { eq(X, Y) -> false()
     , eq(n__0(), n__0()) -> true()
     , eq(n__s(X), n__s(Y)) -> eq(activate(X), activate(Y))
     , activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(X)
     , activate(n__inf(X)) -> inf(X)
     , activate(n__take(X1, X2)) -> take(X1, X2)
     , activate(n__length(X)) -> length(X)
     , inf(X) -> cons(X, n__inf(s(X)))
     , inf(X) -> n__inf(X)
     , s(X) -> n__s(X)
     , take(X1, X2) -> n__take(X1, X2)
     , take(s(X), cons(Y, L)) ->
       cons(activate(Y), n__take(activate(X), activate(L)))
     , take(0(), X) -> nil()
     , 0() -> n__0()
     , length(X) -> n__length(X)
     , length(cons(X, L)) -> s(n__length(activate(L)))
     , length(nil()) -> 0() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {1,2,10,16} by
   applications of Pre({1,2,10,16}) = {3,4,5,8,11,12,13,14,17,19}.
   Here rules are labeled as follows:
   
     DPs:
       { 1: eq^#(X, Y) -> c_1()
       , 2: eq^#(n__0(), n__0()) -> c_2()
       , 3: eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
       , 4: activate^#(X) -> c_4(X)
       , 5: activate^#(n__0()) -> c_5(0^#())
       , 6: activate^#(n__s(X)) -> c_6(s^#(X))
       , 7: activate^#(n__inf(X)) -> c_7(inf^#(X))
       , 8: activate^#(n__take(X1, X2)) -> c_8(take^#(X1, X2))
       , 9: activate^#(n__length(X)) -> c_9(length^#(X))
       , 10: 0^#() -> c_16()
       , 11: s^#(X) -> c_12(X)
       , 12: inf^#(X) -> c_10(X, s^#(X))
       , 13: inf^#(X) -> c_11(X)
       , 14: take^#(X1, X2) -> c_13(X1, X2)
       , 15: take^#(s(X), cons(Y, L)) ->
             c_14(activate^#(Y), activate^#(X), activate^#(L))
       , 16: take^#(0(), X) -> c_15()
       , 17: length^#(X) -> c_17(X)
       , 18: length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L))))
       , 19: length^#(nil()) -> c_19(0^#()) }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
     , activate^#(X) -> c_4(X)
     , activate^#(n__0()) -> c_5(0^#())
     , activate^#(n__s(X)) -> c_6(s^#(X))
     , activate^#(n__inf(X)) -> c_7(inf^#(X))
     , activate^#(n__take(X1, X2)) -> c_8(take^#(X1, X2))
     , activate^#(n__length(X)) -> c_9(length^#(X))
     , s^#(X) -> c_12(X)
     , inf^#(X) -> c_10(X, s^#(X))
     , inf^#(X) -> c_11(X)
     , take^#(X1, X2) -> c_13(X1, X2)
     , take^#(s(X), cons(Y, L)) ->
       c_14(activate^#(Y), activate^#(X), activate^#(L))
     , length^#(X) -> c_17(X)
     , length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L))))
     , length^#(nil()) -> c_19(0^#()) }
   Strict Trs:
     { eq(X, Y) -> false()
     , eq(n__0(), n__0()) -> true()
     , eq(n__s(X), n__s(Y)) -> eq(activate(X), activate(Y))
     , activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(X)
     , activate(n__inf(X)) -> inf(X)
     , activate(n__take(X1, X2)) -> take(X1, X2)
     , activate(n__length(X)) -> length(X)
     , inf(X) -> cons(X, n__inf(s(X)))
     , inf(X) -> n__inf(X)
     , s(X) -> n__s(X)
     , take(X1, X2) -> n__take(X1, X2)
     , take(s(X), cons(Y, L)) ->
       cons(activate(Y), n__take(activate(X), activate(L)))
     , take(0(), X) -> nil()
     , 0() -> n__0()
     , length(X) -> n__length(X)
     , length(cons(X, L)) -> s(n__length(activate(L)))
     , length(nil()) -> 0() }
   Weak DPs:
     { eq^#(X, Y) -> c_1()
     , eq^#(n__0(), n__0()) -> c_2()
     , 0^#() -> c_16()
     , take^#(0(), X) -> c_15() }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   We estimate the number of application of {3,15} by applications of
   Pre({3,15}) = {2,7,8,9,10,11,12,13}. Here rules are labeled as
   follows:
   
     DPs:
       { 1: eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
       , 2: activate^#(X) -> c_4(X)
       , 3: activate^#(n__0()) -> c_5(0^#())
       , 4: activate^#(n__s(X)) -> c_6(s^#(X))
       , 5: activate^#(n__inf(X)) -> c_7(inf^#(X))
       , 6: activate^#(n__take(X1, X2)) -> c_8(take^#(X1, X2))
       , 7: activate^#(n__length(X)) -> c_9(length^#(X))
       , 8: s^#(X) -> c_12(X)
       , 9: inf^#(X) -> c_10(X, s^#(X))
       , 10: inf^#(X) -> c_11(X)
       , 11: take^#(X1, X2) -> c_13(X1, X2)
       , 12: take^#(s(X), cons(Y, L)) ->
             c_14(activate^#(Y), activate^#(X), activate^#(L))
       , 13: length^#(X) -> c_17(X)
       , 14: length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L))))
       , 15: length^#(nil()) -> c_19(0^#())
       , 16: eq^#(X, Y) -> c_1()
       , 17: eq^#(n__0(), n__0()) -> c_2()
       , 18: 0^#() -> c_16()
       , 19: take^#(0(), X) -> c_15() }
   
   We are left with following problem, upon which TcT provides the
   certificate MAYBE.
   
   Strict DPs:
     { eq^#(n__s(X), n__s(Y)) -> c_3(eq^#(activate(X), activate(Y)))
     , activate^#(X) -> c_4(X)
     , activate^#(n__s(X)) -> c_6(s^#(X))
     , activate^#(n__inf(X)) -> c_7(inf^#(X))
     , activate^#(n__take(X1, X2)) -> c_8(take^#(X1, X2))
     , activate^#(n__length(X)) -> c_9(length^#(X))
     , s^#(X) -> c_12(X)
     , inf^#(X) -> c_10(X, s^#(X))
     , inf^#(X) -> c_11(X)
     , take^#(X1, X2) -> c_13(X1, X2)
     , take^#(s(X), cons(Y, L)) ->
       c_14(activate^#(Y), activate^#(X), activate^#(L))
     , length^#(X) -> c_17(X)
     , length^#(cons(X, L)) -> c_18(s^#(n__length(activate(L)))) }
   Strict Trs:
     { eq(X, Y) -> false()
     , eq(n__0(), n__0()) -> true()
     , eq(n__s(X), n__s(Y)) -> eq(activate(X), activate(Y))
     , activate(X) -> X
     , activate(n__0()) -> 0()
     , activate(n__s(X)) -> s(X)
     , activate(n__inf(X)) -> inf(X)
     , activate(n__take(X1, X2)) -> take(X1, X2)
     , activate(n__length(X)) -> length(X)
     , inf(X) -> cons(X, n__inf(s(X)))
     , inf(X) -> n__inf(X)
     , s(X) -> n__s(X)
     , take(X1, X2) -> n__take(X1, X2)
     , take(s(X), cons(Y, L)) ->
       cons(activate(Y), n__take(activate(X), activate(L)))
     , take(0(), X) -> nil()
     , 0() -> n__0()
     , length(X) -> n__length(X)
     , length(cons(X, L)) -> s(n__length(activate(L)))
     , length(nil()) -> 0() }
   Weak DPs:
     { eq^#(X, Y) -> c_1()
     , eq^#(n__0(), n__0()) -> c_2()
     , activate^#(n__0()) -> c_5(0^#())
     , 0^#() -> c_16()
     , take^#(0(), X) -> c_15()
     , length^#(nil()) -> c_19(0^#()) }
   Obligation:
     runtime complexity
   Answer:
     MAYBE
   
   Empty strict component of the problem is NOT empty.


Arrrr..